Has dimension reduction been reduced?
I implemented a sizing algorithm using ENCOG which takes a dataset (calls it A) with multiple functions and reduces it to a dataset (B) with only one function (I need this for time series analysis).
Now my question is, I have a value from B - predicted by time series analysis, is it possible to convert it back to two dimensions like in dataset A?
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Dimension reduction (information compression) is reversible in autoencoders. An autocoder is a common neural network with a narrow layer in the middle. You have, for example, 20 inputs in the first layer, 10 neurons in the middle layer, and 20 more neurons in the last layer. When you train such a network, you force it to compress the information by 10 neurons and then decompress it again, minimizing the error in the last layer (the desired output vector is equal to the input vector). When you use a well-known backpropagation algorithm to train such a network, it performs PCA - Principal Component Analysis. PCA returns uncorrelated functions. It's not very powerful.
By using a more complex algorithm to train the autoencoder, you can force it to perform nonlinear ICA-independent component analysis. ICA returns statistically independent functions. This learning algorithm looks for neural networks with a low degree of complexity with a high generalizability. As a byproduct of regularization, you get the ICA.
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